There is this question(UVa 11212 — Editing a Book):

You have n equal-length paragraphs numbered 1 to n. Now you want to arrange them in the order of 1, 2, . . . , n. With the help of a clipboard, you can easily do this: Ctrl-X (cut) and Ctrl-V (paste) several times. You cannot cut twice before pasting, but you can cut several contiguous paragraphs at the same time — they’ll be pasted in order.

I will not spoil the answer in case you want to solve it too. But I need to prove that for n = 9 (btw this is the n limit) maximum possible answer is 5. I suck at math so I cant prove it, could you help me?

Try to prove: Worst possible situation is A = {9, 8, 7, 6, 5, 4, 3, 2, 1} (I couldn't x_x) If so, Try to prove: Answer of A before is 5 (I am too skill issue that I couldn't find any answer better than 6)

The reason I say it is 5 is the book says it so (Steven Halim, Felix Halim, Suhendry Effendy — Competitive Programming 4 Book 2).

Almost every contest I participate, at the end I say "it was speedforces" and probably most of the experts too. And I thought, why is it the case? So I have a offering, but first I will talk about why I have that offering.

Contests have problem arrangement based on their difficulties. Even if the difficulty of the two adjacent problems were same, amount of people solved first is more than the second one. Thats because of the fact that people have less time every problem they solve. On top of that, the problems hardness increases, so most of the people I know (Including me) gives up when they solve an ok problem. And this makes a pile of people who solved the first x problem but doesn't have time + courage to solve the other problem.

So my offering is because of the fact that the number of people solved problems drops exponentially, making the problem difficulty gap less between C, D and E (maybe even same hardness). So contests may be less speedforces.

Last contest:

https://codeforces.com/problemset/problem/1815/A -1300

https://codeforces.com/problemset/problem/1815/B -2000